In Robertson-Walker universe, light is emitted from a star with spatial coordinates $(r_s,\theta_s,\phi_s)$. It travels radially inwards and is received by an observer situated at the origin $(r=0)$. Show that the ratio of the observed wavelength $\lambda$ to the proper wavelength $\lambda_0)$ is given by $$\lambda /\lambda_0=R(t_2)/R(t_1),$$ where $t_1$ is the time of emision, and $t_2$ is the time of reception.
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